Question

. Example: . Suppose a firm issued a 9% coupon bond (semiannual coupon) 20 years ago. The bond n ow has 10 years left until its maturity date. The bond is selling at $ 750. . But the firm is having financial difficulty. Investors believe that the firm will be able to ma ke good on the remaining interest rate payments but that at the maturity date, the firm w ill be forced into bankruptcy and bondholders will receive only 70% of par value. . Par value: stated ($1,000) vs. believed (70% $1,000) • Calculate yields: Expected YTM Stated YTM Coupon payment $45 $45 Number of semiannual periods 20 periods 20 periods Final payment $700 $1,000 Price $750 $750 . Comparing yields: Expected YTM = ?, Stated YTM = ? FIA301, FALL 2019 Default Risk and Bond Pricing • Example (cont'd.): . Suppose the condition of the firm deteriorates further, and investor now believe that the b ond will pay off only 55% of face value at maturity. Investors now demand an expected yi eld to maturity of 12% (i.e., 6% semiannually). • What is the price of the bond? (n = 20; i = 6; FV = 550; PMT = $45] • What is the stated YTM?

Answer 1

With expected final payment of $750, using the RATE function of Excel,

Expected YTM=11.630275% (Annual) or 5.815138% Semiannual as follows:

Align Clipboard Font fRATE(C7,C8,C9*-1,C2) C10 A В С Formula Values 1 2 Final Payment $700 Given 3 Coupon rate (R) 4 Interest frequency 9% Given Semiannual Given Number of coupon payments a year 5 2 Time to maturity (no. of years) (N) 6 Given 10 7 Number of future coupon payments (t) 8 Amount of coupon payment Given 20 $45 $750.00 5.815138% Given 9 Price Given 10 Expected YTM (Semiannual) 11 Expected YTM (annual) 11.630275% 12

Stated YTM=13.656904% (Annual) or 6.628452% Semiannual as follows:

Clipboard Font Alic fiRATE(C7,C8, C9*-1, C2) C10 A B Formula Values 1 $1,000 2 Final Payment Given 3 Coupon rate (R) 9% Given Interest frequency Number of coupon payments a year Semiannual 4 Given 5 2 6 Time to maturity (no. of years) (N) Given 10 7 Number of future coupon payments (t) Given 20 $45 8 Amount of coupon payment Given $750.00 6.828452% 9 Price Given 10 Stated YTM (Semiannual) 11 Stated YTM (annual) 13.656904% 13

Expecting final payment of 55% only and required YTM (Annual) of 12%, Price of the bond, using PV function of Excel is $687.64 as follows:

clipboard Font Alignm fPV(C7,C5,C6, C2) C8 A. C Formula Values 2 Final Payment (FV) 3 Coupon rate (R) 4 Time to maturity (no. of years) (N) $550 Given 9% Given Given 10 5 Number of future coupon payments (n) 6 Amount of coupon payment (PMT) 7 Required YTM (Semiannual) (i) Given $45 Given 6% Given 8 Price -687.64 10 20

As the Face Value is $1,000 using RATE function of Excel, stated YTM =15.166977% (Annual) or 7.583489% (Semiannual) as given below:

fixRATE(C5,C6, C7*-1, C2) С8 A Formula Values 1 $1,000 2 Final Payment (FV) Given 3 Coupon rate (R) 9% Given 4 Time to maturity (no. of years) (N) Given 10 5 Number of future coupon payments (n) Given 20 $45 Amount of coupon payment (PMT) 6 Given $687.64 7.583489% 7 Price 8 Stated YTM Semiannual Stated YTM Annual 15.166977% 9 10